We sharpen run-time analysis for algorithms under the partial rejection sampling framework. Our method yields improved bounds for: the cluster-popping algorithm for approximating all-terminal network reliability; the cycle-popping algorithm for sampling rooted spanning trees; the sink-popping algorithm for sampling sink-free orientations. In all three applications, our bounds are not only tight in order, but also optimal in constants.
@article{arxiv.1807.01680,
title = {Tight bounds for popping algorithms},
author = {Heng Guo and Kun He},
journal= {arXiv preprint arXiv:1807.01680},
year = {2018}
}